Enroll in one of our FREE online STEM summer camps. Space is limited so join now!View Summer Courses

Georgia Southern University

Problem 1
Problem 2
Problem 3
Problem 4
Problem 5
Problem 6
Problem 7
Problem 8
Problem 9
Problem 10
Problem 11
Problem 12
Problem 13
Problem 14
Problem 15
Problem 16
Problem 17
Problem 18
Problem 19
Problem 20
Problem 21
Problem 22
Problem 23
Problem 24
Problem 25
Problem 26
Problem 27
Problem 28
Problem 29
Problem 30
Problem 31
Problem 32
Problem 33
Problem 34
Problem 35
Problem 36
Problem 37
Problem 38
Problem 39
Problem 40
Problem 41
Problem 42
Problem 43
Problem 44
Problem 45
Problem 46
Problem 47
Problem 48
Problem 49
Problem 50
Problem 51
Problem 52
Problem 53
Problem 54
Problem 55
Problem 56
Problem 57
Problem 58
Problem 59
Problem 60
Problem 61
Problem 62
Problem 63
Problem 64
Problem 65
Problem 66
Problem 67
Problem 68
Problem 69
Problem 70
Problem 71
Problem 72

Need more help? Fill out this quick form to get professional live tutoring.

Get live tutoring
Problem 4

Answer the following questions about the functions whose derivatives are given:

\begin{equation}\begin{array}{l}{\text { a. What are the critical points of } f ?} \\ {\text { b. On what open intervals is } f \text { increasing or decreasing? }} \\ {\text { c. At what points, if any, does } f \text { assume local maximum and }} \\ \quad {\text { minimum values? }}\end{array}\end{equation}

\begin{equation}f^{\prime}(x)=(x-1)^{2}(x+2)^{2}\end{equation}

Answer

see the graph

You must be logged in to like a video.

You must be logged in to bookmark a video.

## Discussion

## Video Transcript

okay, Silver, given this derivative F crime of X is X minus one squared times X plus, two squared and the first thing we want to do this find the critical points. Well, it's easy to see their critical points here. I'm going to be with derivatives. Zero drift. It's never going to be under signed X equals one and X equals negative, too. And then, secondly, we want to give the open intervals where F is increasing or decreasing. So controlling number line you made it to in one we know that is going to change from being increasing that you're decreasing when asked prime changes from being positive to negative. So you want to see where f crime is positive and negative. So if I take a number less than negative too well, I mean, I guess it's not so hard to see that actually have. Crime is always greater than or equal to zero because it's the product of two things that are squared so f prime. It's always going to be increasing unless zero so to the left and negative to F crimes going be positive between aged two and one, coming positive and in greater than one. It's going to be positive. And so if we look at F, it's going to be increasing from negative infinity, the native to it's going to be increasing from negative to one and it's going to be increasing from one to infinity. So what that means is that F actually has no local extreme because it never changes from being increasing to decreasing or decreasing to increasing no local extra see.

## Recommended Questions